Based on the Sanders thin shell theory and Reddy’s higher order shell theory, a general refined shell theory is developed for the analysis of stresses and deformations of pneumatic radial tires of composite construction. For easy and efficient simulation of the tire a piecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to the nonlinear structural problem. Bezier polynomials are used to approximate both the geometry of the surface of reference and displacement fields of the tires. Stress distributions and deformations of the tires subjected to uniform inflation pressure are computed and discussed in details. From comparison of the present results with the numerical predictions by 3D finite element method, it has been shown that the present solution procedure is accurate and applicable to much complicated time-consuming nonlinear analysis for the high quality tire. Based on the Sanders thin shell theory and Reddy’s higher order shell theory, a general refined shell theory is developed for the analysis of stresses and deformations of pneumatic radial tires of composite construction. For easy and efficient simulation of the tire a piecewise Rayleigh-Ritz technique is proposed and applied to get a numerical solution to the nonlinear structural problem. Bezier polynomials are used to approximate both the geometry of the surface of reference and displacement fields of the tires. Stress distributions and deformations of the tires 受受 uniform inflation pressure are computed From comparison of the present results with the numerical predictions by 3D finite element method, it has been shown that the present solution procedure is accurate and applicable to much complicated time-consuming nonlinear analysis for the high quality tire.